%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET115-7 : TPTP v9.3.1. Bugfixed v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:35:49 AM UTC 2026
% Result : Unsatisfiable 0.17s 0.49s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 3
% Syntax : Number of formulae : 8 ( 6 unt; 0 def)
% Number of atoms : 10 ( 9 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 6 ( 4 ~; 2 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 2 ( 0 sgn 1 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_unique_1st_in_pair_of_non_sets,axiom,
first(x) != x,
file('theBenchmark.p',prove_unique_1st_in_pair_of_non_sets) ).
cnf(c_33,plain,
first(x) != x,
inference(clausify,[status(thm)],[prove_unique_1st_in_pair_of_non_sets]) ).
fof(prove_unique_1st_and_2nd_in_pair_of_non_sets3_1,axiom,
ordered_pair(first(x),second(x)) != x,
file('theBenchmark.p',prove_unique_1st_and_2nd_in_pair_of_non_sets3_1) ).
cnf(c_34,plain,
ordered_pair(first(x),second(x)) != x,
inference(clausify,[status(thm)],[prove_unique_1st_and_2nd_in_pair_of_non_sets3_1]) ).
fof(existence_of_1st_and_2nd_4,axiom,
! [VAR_0] :
( first(VAR_0) = VAR_0
| ordered_pair(first(VAR_0),second(VAR_0)) = VAR_0 ),
file('theBenchmark.p',existence_of_1st_and_2nd_4) ).
cnf(c_38,plain,
( first(A) = A
| ordered_pair(first(A),second(A)) = A ),
inference(clausify,[status(thm)],[existence_of_1st_and_2nd_4]) ).
cnf(c_223,plain,
first(x) = x,
inference(resolve,[status(thm)],[c_38,c_34]) ).
cnf(c_222,plain,
$false,
inference(resolve,[status(thm)],[c_33,c_223]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET115-7 : TPTP v9.3.1. Bugfixed v7.3.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.44 % Computer : n008.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Sat Sep 26 07:10:24 UTC 2026
% 0.17/0.45 % CPUTime :
% 0.17/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.45 % Process 3040288 was started by sandbox on n008,
% 0.17/0.45 % Sat Sep 26 07:10:24 2026
% 0.17/0.45 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.17/0.46
% 0.17/0.46 % From the command line: assign(max_seconds, 300).
% 0.17/0.49
% 0.17/0.49 % SZS status Unsatisfiable for theBenchmark
% 0.17/0.49
% 0.17/0.49 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.17/0.49 % Length of proof is 4.
% 0.17/0.49 % Level of proof is 1.
% 0.17/0.49 % Maximum clause weight is 26.000.
% 0.17/0.49 % Given clauses 11.
% 0.17/0.49
% 0.17/0.49 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------